A315532 Coordination sequence Gal.6.662.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

1, 6, 11, 17, 22, 30, 34, 37, 45, 48, 56, 66, 67, 71, 78, 84, 90, 97, 101, 102, 112, 120, 123, 131, 134, 138, 146, 151, 157, 162, 168, 174, 179, 185, 190, 198, 202, 205, 213, 216, 224, 234, 235, 239, 246, 252, 258, 265, 269, 270

Offset

0,2

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Table of n, a(n) for n=0..49.

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Formula

Conjectures from Chai Wah Wu, May 07 2024: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 6*a(n-6) + 6*a(n-7) - 6*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14.

G.f.: (x^14 + 4*x^13 + 2*x^12 + 9*x^11 + 2*x^10 + 17*x^9 - 3*x^8 + 20*x^7 - 3*x^6 + 17*x^5 + 2*x^4 + 9*x^3 + 2*x^2 + 4*x + 1)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)

Crossrefs

Sequence in context: A315529 A315530 A315531 * A315533 A063901 A315534

Adjacent sequences: A315529 A315530 A315531 * A315533 A315534 A315535

Keyword

nonn

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Status

approved